The unshaven valley

A super model. Simple, beautiful, but not your reality.

If you want to test quantum gravity, the physics of the early universe is promising, very promising. Back then, energy densities were high, curvature was large, and we can expect effects were relevant that we’d never see in our laboratories. It is thus not so surprising that there exist many  descriptions of the early universe within one or the other approach to quantized gravity. The intention is to test compatibility with existing data and, ideally, make new predictions and arrive at new insights.

In a recent paper, Burgess, Cicoli and Quevedo contrasted a number of previously proposed string theory models for inflation with the new Planck data (arXiv:1306.3512 [hep-th]). They conclude that by and large most of these models are still compatible with the data because our observations seem to be fairly generic. In the trash bin goes everything that predicted large non-Gaussianities, and the jury is still out on the primordial tensor modes, because Planck hasn’t yet published the data. It’s the confrontation of models with observation that we’ve all been waiting for.

The Burgess et al paper is very readable if you are interested in string inflation models. It is valuable for pointing out difficulties with some of these approaches that gives the reader a somewhat broader perspective than just data fitting. Interesting for a completely different reason is the introduction of the paper with a subsection “Why consider such complicated models?” that is a forward defense against Occam’s razor. I want to spend some words on this.

Occam’s razor is the idea that from among several hypotheses with the same explanatory power the simplest one is the best, or at least the one that scientists should continue with. This sounds reasonable until you ask for definitions of the words “simple” and “explanatory power”.

“Simple” isn’t simple to define. In the hard sciences one may try to replace it with small computational complexity, but that neglects that scientists aren’t computers. What we regard as “simple” often depends on our education and familiarity with mathematical concepts. Eg you might find Maxwell’s equations much simpler when written with differential forms if you know how to deal with stars and wedges, but that’s really just cosmetics. Perceived simplicity also depends on what we find elegant which is inevitably subjective. Most scientists tend to find whatever it is that they are working on simple and elegant.

Replacing “simple” with the number of assumptions in most cases doesn’t help remove the ambiguity because it just raises the question what’s a necessary assumption. Think of quantum mechanics. Do you really want to count all assumptions about convergence properties of hermitian operators on Hilbert-spaces and so on that no physicist ever bothers with?

There’s one situation in which “simpler” seems to have an unambiguous meaning, which is if there are assumptions that are just entirely superfluous. This seems to be the case that Burgess et al are defending against, which brings us to the issue of explanatory power.

Explanatory power begs the question what should be explained with that power. It’s one thing to come up with a model that describes existing data. It’s another thing entirely whether that model is satisfactory, again an inevitably subjective notion.

ΛCDM for example fits the available data just fine. For the theoretician however it’s a highly unsatisfactory model because we don’t have a microscopic explanation for what is dark matter and dark energy. Dark energy in particular comes with the well-known puzzles of why it’s small, non-zero, and became relevant just recently in the history of the universe. So if you want to shave model space, should you discard all models that make additional assumptions about dark matter and dark energy because a generic ΛCDM will do for fitting the data? Of course you shouldn’t. You should first ask what the model is supposed to explain. The whole debate about naturalness and elegance in particular hinges on the question of what requires an explanation.

I would argue that models for dark energy and dark matter aim to explain more than the available data and thus should not be compared to ΛCDM in terms of explanatory power. These models that add onto the structure of ΛCDM with “unnecessary” assumption are studied to make predictions for new data, so that experimentalists know what to look for. If new data comes in, then what requires an explanation can change one day to the next. What was full with seemingly unnecessary assumptions yesterday might become the simplest model tomorrow. Theory doesn’t have to follow experiment. Sometimes it’s the other way round.

The situation with string inflation models isn’t so different. These models weren’t constructed with the purpose of being the simplest explanation for available data. They were constructed to study and better understand quantum effects in the early universe, and to see whether string theoretical approaches are consistent with observation. The answer is, yes, most of them are, and still are. It is true of course that there are simpler models that describe the data. But that leaves aside the whole motivation for looking for a theory of quantum gravity to begin with.

Now one might try to argue that a successful quantization of gravity should fulfill the requirement of simplicity. To begin with, that’s an unfounded expectation. There really is no reason why more fundamental theories should be simpler in any sense of the word. Yes, many people expect that a “theory of everything” will, for example, provide a neat and “simple” explanation for the masses of particles in the standard model and ideally also for the gauge groups and so on. They expect a theory of everything to make some presently ad-hoc assumptions unnecessary. But really, we don’t know that this has to be the case. Maybe it just isn’t so. Maybe quantum gravity is complicated and requires the introduction of 105 new parameters, who knows. After all, we already know that the universe isn’t as simple as it possibly could be just by virtue of existing.

But even if the fundamental theory that we are looking for is simple, this does not mean that phenomenological models on the path to this theory will be of increasing simplicity. In fact we should expect them to be less simple by construction. The whole purpose of phenomenological models is to bridge the gap between what we know and the underlying fundamental theory that we are looking for. On both ends, there’s parsimony. In between, there’s approximations and unexplained parameter values and inelegant ad-hoc assumptions.

Phenomenological models that are not strictly derived from but normally motivated by some approach to quantum gravity are developed with the explicit purpose to quantify effects that have so far not been seen. This means they are not necessary to explain existing data. Their use is to identify promising new observables to look for, like eg tensor modes or non-Gaussianity.

In other words, even if the fundamental theory is simple, we’ll most likely have to go through a valley of ugly, not-so-simple, unshaven attempts. Applying Occam’s razor would cut short these efforts and greatly hinder scientific progress.

It’s not that Occam’s razor has no use at all, just that one has to be aware it marks a fuzzy line because scientists don’t normally agree on exactly what requires an explanation. For every model that offers a genuinely new way of thinking about an open question, there follow several hundred small variations of the original idea that add little or no new insights. Needless to say, this isn’t particularly conductive to progress. This bandwagon effect is greatly driven by present publication tactics and largely a social phenomenon. Occam’s razor would be applicable, but of course everybody will argue that their contribution adds large explanatory value, and we might be better of to err on the unshaven side.

If a ball rolls in front of your car, the simplest explanation for your observation, the one with the minimal set of assumption, is that there’s a ball rolling. From your observation of it rolling you can make a fairly accurate prediction where it’s going. But you’ll probably brake even if you are sure you’ll miss the ball. That’s because you construct a model for where the ball came from and anticipate new data. The situation isn’t so different for string inflation models. True, you don’t need them to explain the ball rolling; the Planck data can be fitted by simpler models. But they are possible answers to the question where the ball came from and what else we should watch out for.

In summary: Occam’s razor isn’t always helpful to scientific progress. To find a fundamentally simple theory, we might have to pass through stages of inelegant models that point us into the right direction.